00:02
In this problem, we are asked to explain why conjectures that work for even numbers do not necessarily always work for other types of numbers, like odd numbers.
00:14
Well, the biggest reason for this is that even numbers are unique in the fact that all even numbers above two are composite.
00:23
There are no numbers, no even numbers greater than two, that are prime.
00:31
They all at least have another factor of two because all those numbers are divisible by two.
00:36
So that's one of the major factors as to why conjectures work for even numbers and not other numbers.
00:42
One example of conjecture that only works for even numbers is this one.
00:47
Any even number can be written as the sum of two odd numbers.
00:53
For example, i can take 12 and write it as the sum of seven and five.
00:59
Seven and five are both odd.
01:01
I add them together and i get an even number.
01:04
Same thing with the number 18...